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I'm writing about a setting where the people have some advanced theoretical knowledge, but as yet limited manufacturing ability; in particular, they do not yet have metallurgy, but they are trying to make some fairly complex machines such as spinning wheels, wheelbarrows, pottery wheels and watermills, that require precise moving parts that can withstand significant stress; in our world, these had to wait until they could be made from metal.

But one thing they do have access to is a magical power to shape stone. That eliminates the usual disadvantage of stone for such purposes, that it cannot easily be worked into precise, complex shapes.

There is still the problem that, while some kinds of stone (e.g. flint) are hard and resistant to wear, stone always has poor tensile strength. For some applications, this might be overcome simply by using a sufficient thickness of it, but gears need to fit in the machinery they are driving, and wheels and axles cannot be arbitrarily heavy and still move around.

Given the ability to shape any kind of stone into arbitrarily precise, complex shapes, could the above artifacts be made to work?

My current best guess is that medium-duty things like pottery wheels can work, just by making all the moving parts thick enough to withstand the relatively light stresses placed on them; a pottery wheel doesn't have to withstand forces above a few hundred newtons, I think. But a watermill? It seems to me that the gears connecting the mill to the load it drives, need to withstand enormous force, such that if they were made of stone, the gear teeth would quickly break off; for that application, there is no alternative to using metal, because you need both hardness and tensile strength.

Is that estimate correct, or am I missing something? Is there an easy way to do quantitative estimates for this?

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    $\begingroup$ Yes, if they managed to make machines with complex gears from wood, they can do it with stone too... And stone is probably easier to shape than wood, just look at the difference between wood statues and marble or rock statues.... Wood takes way more skill and more advanced tools. $\endgroup$
    – user85880
    Commented Jun 27, 2021 at 18:06
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    $\begingroup$ "In our world, these had to wait until they could be made from metal": No they didn't. They were made of wood. You won't find any "spinning wheels, wheelbarrows, pottery wheels and watermills" made of metal until the 19th century; and even today wheelbarrows are quite often made of wood, and pottery wheels very often. Wood is very much better for this kinds of applications that stone, at it is both lighter and stronger in tension. (Plus is it much easier to work and shape.) $\endgroup$
    – AlexP
    Commented Jun 27, 2021 at 19:20
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    $\begingroup$ Wood, for high torque low speed systems, and leather belts on pulleys for low torque high speed applications. Metal is only needed if you want to make something that is ultra high accuracy, like a chronometer, or required both high speed and high torque. A metalworking Lathe, for example. $\endgroup$
    – PcMan
    Commented Jun 27, 2021 at 21:47
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    $\begingroup$ Note that one almost never needs to use gears!! Gears only provide an easy and compact means of changing he speed and torque of your drive system. A Watermill, for example, can be build just fine with no gears at all, simply by scaling the waterwheel to be rather absurdly large. $\endgroup$
    – PcMan
    Commented Jun 27, 2021 at 21:50
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    $\begingroup$ Very accurate items can be made from wood. Slide rules used to be made from wood, and the better made ones are more accurate than metal ones because metal changes size with temperature. $\endgroup$
    – NomadMaker
    Commented Jun 28, 2021 at 5:08

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Actually, in history everything you mention was made of wood, especially any large wheels like the machinery of watermills or windmills. Pottery wheels were completely wood as well. The only metal you may find in historical waterwheel could be nails helping to hold it together... but even those may be replaced with proper wooden pegs.

In fact, you do not want large wheels made of stone. they would be much more difficult to turn (being much, much heavier) and so would require way more energy applied. Plus, there would be massive problem of obtaining and transporting those huge slabs you want to make wheels from - waterwheels were as large as 8-10m diameter! Those were made from wooden framing... imagine this made from stone - I doubt you will find a material for the axle (as the wheel has to hang on a central axle). Traditionally axles were made from wood.

I'm not sure (I'm not material engineer) but I believe wood is actually more resilient in such applications than stone. After all, roof constructions were made entirely of wood even in stone buildings (remember the oak roof of Notre Dame of Paris that burned down in 2019?)

Windmill machinery example: https://www.alamy.com/the-netherlands-internal-mechanism-of-a-traditional-windmill-close-up-image216205468.html

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    $\begingroup$ wood is better for gears because it is strong against sheer forces, is was used for roof framing for the same reason. wood was used for roof cladding because it was cheap, stone worked better but was more expensive. $\endgroup$
    – John
    Commented Jun 28, 2021 at 5:17
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    $\begingroup$ You would find stone used in e.g. flour mills, but just as the last part that actually does the grinding. (Thus "stone-ground" flour.) The rest would probably be made of wood. $\endgroup$
    – jamesqf
    Commented Jun 28, 2021 at 6:07
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    $\begingroup$ You're missing a closing parenthesis towards the end of your second paragraph. $\endgroup$
    – Kat
    Commented Jun 28, 2021 at 14:05
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    $\begingroup$ @Nosajimiki no more of a fire hazard than the wooden axle on a wagon, water wheel, or lathe. entirely wooden pottery wheels were quite common historically. of course you can grease them too. $\endgroup$
    – John
    Commented Jun 29, 2021 at 1:26
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    $\begingroup$ For the actual teeth, apple wood, seasoned 9 years, was preferred for its hardness. (And even then, teeth were replaceable, fitting into tapers in the wheel rim ( or for pinions, as bars between two rims - see "lantern pinion") $\endgroup$
    – user_1818839
    Commented Jun 29, 2021 at 11:43
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If you can magically shape it, then yes

Let's take limestone for example... it is a very common kind of stone that can be found all over the world; so, your people are pretty much guaranteed access to large amounts of it. Despite its normally soft nature, certain limestones can have very similar tensile properties to aluminum despite its lower Modulus of Rupture.

High-Density Limestone:

  • Elastic (Young's, Tensile) Modulus: 77 GPa
  • Shear Modulus: 30 GPa
  • Ultimate Tensile Strength: 100 MPa

Aluminum alloy:

  • Elastic (Young's, Tensile) Modulus: 69 GPa
  • Shear Modulus: 30 GPa
  • Ultimate Tensile Strength: 110 MPa

However, part of why its Modulus of Rupture is so much lower is because of the natural imperfections as explained in (David R's answer), but if you can magically shape stone, then it means that you can shape these imperfections out of it making it much stronger than natural stone. Since limestone is made mostly out of calcium carbonate, it means that once it is properly shaped and compressed, it would have about the same material properties as snail shell or homogenized synthetic marble... which are both by comparison very tough.

So with a little bit of magic and experimentation, it is likely that your people could turn even humble limestone into viable gears. Your gears might need to be a slightly bulkier than their metallic counterparts, but for their weight they should perform just fine.

Part of why this will be fine is that metal gears or belt drives were not preferred for things like grain mills or potter's wheels until the late industrial era, but they were necessary for a wide range of other ancient inventions where you needed more rigidity than wood or linen could supply. So instead of worrying about how to replace large scale metal gears with stone, your chief concern will be replacing the kinds of smaller gears you would have seen in various time-keeping devices, odometers, calculating machines, windlasses and ratchets, certain textile machines, certain water lifting machines, and automata. For most of these, you need stiff a lot more than your need strong.

So actually needing something as tough as metal will not be common, but it will still be available when needed in the form of Sapphire. Sapphire has a flexural strength of 350 to 390 MPa compared to bronze which ranges from 65-700MPa. That said, these figures are based on modern bronze alloys, not historical bronze which would have likely all been in the lower range of this spectrum. Also, 350 to 390 is only as good as natural sapphire is. If you can shape out the impurities, then you could get something closer to synthetic sapphire can which can reach 1090 MPa.

Sources:

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    $\begingroup$ Limestone is a whole family of rock types and they are extremely diverse. Some are strong and resilient... but chalk is a type of limestone too... $\endgroup$
    – Archelaos
    Commented Jun 28, 2021 at 21:28
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    $\begingroup$ Shear modulus and elastic modulus are both measures of stiffness not strength, and is largely irrelevant. Also the tensile strength of aluminum used in anything experiencing loading is about three times what you have listed, so you should check your numbers. You should be looking at Modulus of Rupture (aka bending strength) which is ~400 for the strongest limestone, 10,000 for pine, 28,500 PSI for aluminum alloy, and 65,000 for bronze. HUGE difference. Your other big problem is fatigue failure, which is a big issue for stone. $\endgroup$
    – John
    Commented Jun 29, 2021 at 1:43
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    $\begingroup$ @John Nope, natural limestone goes up to a Modulus of Rupture of about 3000 PSI, but snail shell which is basically just really pure and well formed limestone can exceed 8000. While this sounds inferior to the other materials you listed, where small gears are concerned, your limit is the lesser of the Shear Modulus or Modulus of Rupture because shearing deformation will cause them to jam even if they don't break. Since pine has a Shear Modulus of just 900 PSI, it will encounter problems when used in high precision gears before limestone. This is why it was only used in big mill gears. $\endgroup$
    – Nosajimiki
    Commented Jun 29, 2021 at 3:44
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    $\begingroup$ Also, most of the pre-industrial inventions that actually used metal gears were actually pretty low stress jobs anyway. If your clock, odometer, or bobbin is experiencing more than a couple of of PSI on its gears, you are doing something very wrong. $\endgroup$
    – Nosajimiki
    Commented Jun 29, 2021 at 3:48
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    $\begingroup$ I find the numbers you cited surprising too, but let's assume they're correct. But you omitted one factor that would, I think, be a huge issue for limestone: abrasion resistance. Wood-on-wood is actually pretty good in this regard, so is plastic-on-plastic, and specialised ceramics excel. But even hard limestone is notorious for leaving white traces on anything you rub it against, so surely two gears made from limestone would quickly grind each other to powder when moving under any nontrivial load? –Not sure how much lubrication would help with this. $\endgroup$
    – leftaroundabout
    Commented Jun 29, 2021 at 9:36
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Speaking from a sculpture perspective: when working with stone, a lot of thought has to go into thinking about how to get the shape without cracking the stone. A lot of stone has hidden cracks in it. Imperfections and included other materials weaken the stone unexpectedly. A lot of stone has grain along which it breaks easier. Thus, when you look at old sculpture, there are very few unsupported parts. Legs have other things like tree trunks, little kids, fauns, etc. next to them to give more support. Arms are held close to the body so that they won't break off. Old Greek and Roman sculpture had the arms made from separate blocks and attached with internal bars or some other banding. Other male parts that stick out were also made from separate blocks and attached. It is only recent sculpture made via grinding where you can find unsupported stone and those are much more fragile and have to be kept in protected environments so that accidents don't break them.

In short, gearing which is all points sticking out, is not good for stone. The probability is very strong that the points will break off.

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    $\begingroup$ That's why sculptors love Carrara marble so much. It has large areas of almost uniform composition. Pure white without imperfections that make sculpting difficult. $\endgroup$
    – Archelaos
    Commented Jun 28, 2021 at 21:34
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    $\begingroup$ Even so, the Carrara marble quarries have a lot of broken off blocks. Just look at the pictures from the quarries to see veins of other materials that have to be avoided, etc. $\endgroup$
    – David R
    Commented Jun 28, 2021 at 22:39
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Use belts and pulleys.

pulley wheel

https://studentlesson.com/belt-pulley-definiton-functions-types-parts-working/

Depicted: metal pulley wheels. Stone would be fine for this use. A stone pulley wheel would experience only compressive forces, from the belt. It is easy to replace broken belts. It is easy to increase the tackiness of the stone wheel with the belt using belt dressings.

But: I was not able to find a pulley driven millstone! Either there is some serious advantage to gears or drawback to pulleys and belts, or my google fu is letting me down.

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    $\begingroup$ With gears you can drive the torque higher before it starts to slip. That might be an advantage when building a mill, where the millstone should apply a lot of force to grind as much grain at once as possible. $\endgroup$
    – Robyn
    Commented Jun 28, 2021 at 2:33
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    $\begingroup$ pulley wheel still experience tension and sheer force, also the heavier your wheels the less efficient belt driven pullets get. you won't find a belt driven mill because belts can't deliver high torque because they can only deliver power up to the that of the static friction, usually far less. $\endgroup$
    – John
    Commented Jun 28, 2021 at 5:10
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    $\begingroup$ @Robyn In a traditional mill the millstones don't actually touch; the gap between them controls the fineness of the flour. The torque applied to the stones is only one of a number of limiting factors. (If they do touch big bits of wood start breaking). $\endgroup$
    – Paul Johnson
    Commented Jun 28, 2021 at 12:34
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    $\begingroup$ You are probably having a hard time finding historical examples because the word you are looking for is a "belt drive". They were used in ancient Babylon, Assyria, and China for various things. They are also featured in some of Leonardo da Vinci's drawings; so, Europeans knew about them... they were just not the mechanism of choice. The big problem you will run into though is stretching. Drivebelts normally contain chain or wire to keep it from stretching and losing friction with the wheels; so, the no metal thing could be a problem here. $\endgroup$
    – Nosajimiki
    Commented Jun 28, 2021 at 17:40
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    $\begingroup$ We have the Mill City Museum here in Minneapolis, and it's INSANE the number of belts they had driving everything in that place. One water wheel (the oldest ones wood) ran hundreds of belts powering everything in the plant. Then each different plant had another wheel. $\endgroup$
    – DWKraus
    Commented Jun 28, 2021 at 22:22
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Using stone made gears would be problematic.

The first problem is wear. The stone would easily wear away. The second problem is stone is strong in compression but weak in tension and bending. Gear teeth experience a lot a bending stresses. The gear teeth will most likely fail very easily and very early.

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    $\begingroup$ Some stones like granite (or more or less pure quartz) are very hard which should reduce wear a lot. $\endgroup$
    – Michael
    Commented Jun 29, 2021 at 6:20
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In addition to the static weakness of stone in tension, you also have the issue of crack propogation. Repeated impacts will cause cracks to develop and grow over time.

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Tensile strengths:

  • Silica: 4,000 MPa to 7,000 MPa

  • High-density polyethylene: ~30 MPa

  • PA-11 Nylon: ~50 MPa

  • PA-6 Nylon (fiber): ~600 MPa

  • Aluminium alloy 2014-T6: ~450 MPa

  • SAE 304 Stainless Steel: ~600 MPa

  • Ti-6Al-4V Titanium alloy: ~900 MPa

Usually we can rarely get glass to be that strong, because any small cracks and imperfections in it will grow under strain until it either cracks or shatters. An atom-perfect perfect window pane is basically indestructible to bulk forces until it gets scratched, and only then does it become as fragile as glass usually is.

But "given the ability to shape any kind of stone into arbitrarily precise, complex shapes"? Sand is just lots of small pieces of rock, and most of those are silica. You could make a packed cotton-like material of super-fine glass fibres, or a single solid slab, or a lattice akin to metal foam, and then you could fill it with something soft like soapstone and cover it with something hard like granite to keep it from ever getting scratched.

Forget about making gears: You could turn the beach into a single massive fibreglass arcology stretching all the way to the edge of the sky.

enter image description hereenter image description here

Larger sizes: https://i.sstatic.net/zIumZ.png, https://i.sstatic.net/yTUT5.jpg

Art source: https://www.artstation.com/artwork/g2QNG

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    $\begingroup$ This might be of further interest when it comes to creating material - in this case concrete not fibreglass: "It’s been known for a while that the volcanic sand used in Roman concrete and mortar made their buildings last for so long. Now a new study by a group of engineers and engineering researchers has discovered the precise recipe that made the Roman concrete endure much longer than concrete used today." see ancient-origins.net/news-history-archaeology/… $\endgroup$
    – Risadinha
    Commented Jun 30, 2021 at 12:45
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if they were made of stone, the gear teeth would quickly break off

The constant friction would grind down the teeth until they're too small to fit in the gears.

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    $\begingroup$ Suprised someone upvoted it, I thougth problems of the answer is selfevident, but seems not the case. Metals also have friction and wear as well - and to solve that we use grease and the same solutions are applicable to stone as well. So as someone really has to read about gears and why they have special profiles of teath(for rolling actions of contact surfaces, ideal cases they do not slide against each other), etc etc. It such a non answer. Not saying stone has no problems, but op handwavium is too strong for them to be a big obstacle. $\endgroup$
    – MolbOrg
    Commented Jul 7, 2021 at 10:01
  • $\begingroup$ @MolbOrg the main problem with metal gears is heat, and the expansion which heat causes. And if you don't believe me about friction grinding down stone, just look at the teeth in the skeletons of early agriculturalists; they've all ground down by the grit in the stone-ground wheat. $\endgroup$
    – RonJohn
    Commented Jul 7, 2021 at 10:43

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